I’ve always found scratch cards rather interesting. In the newsagents where I live, there are usually about eight of them at the till. Each has a different prize, at a different price, with different odds of winning.
With so many variations to choose from, I’ve often wondered whether it’s actually possible to make a “perfect” choice – to choose the scratch card that is, by some objective measure, the best value for money - and if so, how would one go about it?
My first guess would be to go for the one with the smallest prize. There’s a lot of evidence that people have a tendency to pay too much for lottery ticket- type investments: those with a small chance of a very large profit. I’ve not done the maths, but I wouldn’t be that surprised if scratch cards are priced accordingly. However, what about comparing more complicated variations?
For example:
Scratch card A: “Win £1,000 a month for the rest of your life!”
Sounds great. But is this better than:
Scratch card B: “Win £250,000 today!”??
For simplicity, let’s assume that both scratch cards have the same odds of winning. Should I buy scratch card A or scratch card B?
The maths might go something like this:
Consider scratch card A: According to the Office for National Statistics, as a 42-year-old man living in England I should expect to live to about 80. So that’s 38 years of monthly payments of £1,000, which would add up to about £450,00 over my lifetime.
£450,000 is clearly more than the £250,000 winnings of scratch card B, so if the odds of winning both scratch cards are the same, I should opt for scratch card A, right?
But there is also a lot to be said for having the money up front rather than paid out gradually over my lifetime. I could, after all, put the £250,000 from winning scratch card B in a savings account, take out £1,000 a month, while at the same time earning interest on the money left in the account.
In fact, if I think I can earn an interest rate of, say, 4 per cent a year, I could take out £1,000 per month until I’m 80 and there would still be nearly £100,000 left over at the end!
Actually, earning 4 per cent interest a year, I’d only need about £225,000 upfront to fund the £1,000 monthly payments until I’m 80 with no money left over at the end (in actuarial terms we say the “present value” of the prize of scratch card A is £225,000).
£225,000 is less than £250,000, so now scratch card B is looking like a better option.
Also 38 years is a long time. How certain am I that the scratch card company (or whoever is ultimately standing behind the promise) will be around for all that time? This makes scratch card A even less appealing. And so on.
This multi-dimensional approach to estimating value is a hugely important part of institutional investing.
Take the £1.7 trillion invested in Defined Benefit (DB) pension funds, which I briefly discuss in my first post. DB pension funds pay a pension to retired employees. The pension amount is calculated using a formula, usually related to how long the employee worked for the company, how much they earned and some other factors that I won’t cover here.
A company needs to know how much money to set aside to pay these pensions, so that the pension fund doesn’t run out of money before all the pensions have been paid.
The approach they follow to valuing this promise is similar to the approach I outlined for scratch card A: estimate the payments that will be paid to members of the scheme in each year until the last member dies. Then calculate how much they need to put aside today to fund those payments, assuming a rate of interest on the money put aside in the pension fund.
What can we take away from this when thinking about our own finances? A crucial first step of successful financial decision making is a shift of mindset - from thinking about value as a one-dimensional thing, measured only in pounds and pence, to a multi-dimensional thing that also depends on timing and certainty. This then equips us to begin to plan for future evens with an uncertain cost, such as our retirement or our childrens’ education, or whether to buy something with an uncertain payout (like insurance).
In future posts I’ll begin to flesh out some of the concepts raised here in more detail and explain further how they can help us make better financial decisions.
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